When I went to public High School, in our English classes we always did a particular type of literature each report period. One fiction, one biography, one Shakespere, and one Bible. The Bible sections were always taught as Bible-as-literature, and provided the class with those oft-alluded-to things that you find in other literature, so you could understand them better. To understand Shakespere, for instance, you need to know the Bible, or at least the events described in it, as well as Greek and Roman mythology. Learning what the Bible said in this manner never caused a problem with anyone that I remember.

The Bible SHOULD be taught as literature in public schools. It's nearly impossible to completely understand the great works of Western literture or even the writings of our American Founding Fathers without the Bible as a referance point. The Bible has had more impact on every aspect of Westernm culture than literally anything else. To completely ignore that fact is to actively invite ignorance in America's youth.